unit conversions and dimensional analysis. measurements in physics - si standards (fundamental...
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Unit Conversions and Dimensional Analysis
Measurements in physics - SI Standards (fundamental units)
Fundamental units: length – meter (m) time – second (s)
mass - kilogram (kg) temperature - kelvin (K)
current – ampere (A)
luminous Intensity - candela (cd)
Amount of substance – mole (mol) – 6.02 x 1023
Derived units: combinations of fundamental units
speed (v) = distance/time
acceleration (a) = velocity / time
force (F) = mass x acceleration
energy (E) = force x distance
charge (Q) = current x time
units: m/s
units: m/s/s = m/s2
units: kgm/s2 = N (Newton)
units: kgm2/s2 = Nm = J (Joule)
units: As = C (Coulomb)
1.3 The Role of Units in Problem Solving
THE CONVERSION OF UNITS
1 ft = 0.3048 m
1 mi = 1.609 km
1 hp = 746 W
1 liter = 10-3 m3
1.3 The Role of Units in Problem Solving
Example 1 The World’s Highest Waterfall
The highest waterfall in the world is Angel Falls in Venezuela,with a total drop of 979.0 m. Express this drop in feet.
feet 3212meter 1
feet 281.3meters 0.979 Length
Since 3.281 feet = 1 meter, it follows that
(3.281 feet)/(1 meter) = 1
1.3 The Role of Units in Problem Solving
1.3 The Role of Units in Problem Solving
gfg
gfg 15
15
1021
101)0.2(
A typical bacterium has a mass of about 2.0 fg. Express this measurement in terms of grams and kilograms.
We know 1 fg = 10-15 g and 1 kg = 103 g
kgg
kgg 18
315 100.2
101
1)102(
1.3 The Role of Units in Problem Solving
Reasoning Strategy: Converting Between Units
1. In all calculations, write down the units explicitly.
2. Treat all units as algebraic quantities. When identical units are divided, they are eliminated algebraically.
3. Use the conversion factors located on the pagefacing the inside cover. Be guided by the fact that multiplying or dividing an equation by a factor of 1does not alter the equation.
1.3 The Role of Units in Problem Solving
Example 2 Interstate Speed Limit
Express the speed limit of 65 miles/hour in terms of meters/second.
Use 5280 feet = 1 mile and 3600 seconds = 1 hour and 3.281 feet = 1 meter.
second
feet95
s 3600
hour 1
mile
feet 5280
hour
miles 651
hour
miles 65 Speed
second
meters29
feet 3.281
meter 1
second
feet951
second
feet95 Speed
1.3 The Role of Units in Problem Solving
DIMENSIONAL ANALYSIS
[L] = length [M] = mass [T] = time
221 vtx
Is the following equation dimensionally correct?
TLTT
LL 2
1.3 The Role of Units in Problem Solving
Is the following equation dimensionally correct?
vtx
LTT
LL